Hi @Paul Marsh ,
One option to secure the keys and connection strings to your azure services would be to use Azure Key Vault to store it as secrets. You can also store it as keys in the Key Vault if you want encryption.
Then you can maintain the mappings between the service key names and the Key Vault secrets/keys names in Table Storage. You can then have a service in your application that will access the table to get the Key Vault secret names and access the Key Vault to get the secrets during runtime if you have set the required access policies.
Link: https://learn.microsoft.com/en-us/azure/key-vault/general/about-keys-secrets-certificates.
Hope this helps!